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Whenever two or more events happen at the same time, i.e., when we use the
word “and,” you will have to decide if the events are independent
or dependent.
Examples 6 and 7 are examples of Independent probabilities. The outcome of
the first event does not affect the probability of the second. Coin tosses are
independent. They cannot affect each other's probabilities; the probability
of each toss is independent of a previous toss and will always be 1/2. Separate
drawings from a deck of cards are independent events ONLY if you put the cards
back.
Dependent events are the opposite. The probability of the second event is affected by the first event. An example of a dependent event is drawing a card
from a deck but not returning it. By not returning the card, you've decreased
the number of cards in the deck by 1, and you've decreased the number of whatever
kind of card you drew. If you draw an ace of spades, then there are 1 fewer
aces and 1 fewer spades.
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